Asif1234 wrote:
A manufacturer can save x dollars per unit in production costs by overproducing in certain seasons. If storage costs for the excess are y dollars per unit per day ) ( y x > , which of the following expresses the maximum number of days that n excess units can be stored before the storage costs exceed the savings on the excess units?
(A) x − y (B) n(x-y) (C) x/y (D) xn/y (E) x/yn
Question: A manufacturer can save \(x\) dollars per unit in production costs by overproducing in certain seasons. If storage costs for the excess are \(y\) dollars per unit per day \((y > x)\), which of the following expresses the maximum number of days that \(n\) excess units can be stored before the storage costs exceed the savings on the excess units?
Amount saved per unit = \($x\)
=> Amount saved for \(n\) units = \($(nx)\)
Extra cost per unit per day = \($y\)
=> Extra cost for \(n\) units per day = \($(ny)\)
Let the required number of days in storage be \(d\)
=> Extra cost for \(n\) units in \(d\) days = \($(nyd)\)
Thus, for storage costs to remain less than or be equal to the savings on the excess units, we have:
\(nyd ≤ nx\)
\(=> d ≤ x/y\)
Thus, maximum number of days = \(x/y\)
Answer C
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